A self adjusting multirate algorithm for robust time discretization of partial differential equations. (1st April 2020)

• Record Type: Journal Article
• Authors: Bonaventura, L.; Casella, F.; Carciopolo, L. Delpopolo; Ranade, A.
• Is Part Of: Computers & mathematics with applications. Volume 79:issue 7(2020)
• Page Start: 2086
• Page End: 2098
• Publication Date: 2020-04-01
• Subjects: Multirate -- Hyperbolic equations -- Stiff problems; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2019.11.023
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We show the distinctive potential advantages of a self adjusting multirate method based on diagonally implicit solvers for the robust time discretization of partial differential equations. The properties of the specific ODE methods considered are reviewed, with special focus on the TR-BDF2 solver. A general expression for the stability function of a generic one stage multirate method is derived, which allows to study numerically the stability properties of the proposed algorithm in a number of examples relevant for applications. Several numerical experiments, aimed at the time discretization of hyperbolic partial differential equations, demonstrate the efficiency and accuracy of the resulting approach.